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Energy budget in internal wave attractor experiments

Published online by Cambridge University Press:  15 October 2019

Géraldine Davis ,
Thierry Dauxois Open the ORCID record for Thierry Dauxois [Opens in a new window] ,
Timothée Jamin  and
Sylvain Joubaud Open the ORCID record for Sylvain Joubaud [Opens in a new window]
Géraldine Davis*
Affiliation:
Univ Lyon, ENS de Lyon, Univ Claude Bernard, CNRS, Laboratoire de Physique, F-69342 Lyon, France
Thierry Dauxois*
Affiliation:
Univ Lyon, ENS de Lyon, Univ Claude Bernard, CNRS, Laboratoire de Physique, F-69342 Lyon, France
Timothée Jamin*
Affiliation:
Univ Lyon, ENS de Lyon, Univ Claude Bernard, CNRS, Laboratoire de Physique, F-69342 Lyon, France
Sylvain Joubaud*
Affiliation:
Univ Lyon, ENS de Lyon, Univ Claude Bernard, CNRS, Laboratoire de Physique, F-69342 Lyon, France
*
†Email addresses for correspondence: [email protected], [email protected], [email protected], [email protected]
†Email addresses for correspondence: [email protected], [email protected], [email protected], [email protected]
†Email addresses for correspondence: [email protected], [email protected], [email protected], [email protected]
†Email addresses for correspondence: [email protected], [email protected], [email protected], [email protected]
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Abstract

The current paper presents an experimental study of the energy budget of a two-dimensional internal wave attractor in a trapezoidal domain filled with uniformly stratified fluid. The injected energy flux and the dissipation rate are simultaneously measured from a two-dimensional, two-component, experimental velocity field. The pressure perturbation field needed to quantify the injected energy is determined from the linear inviscid theory. The dissipation rate in the bulk of the domain is directly computed from the measurements, while the energy sink occurring in the boundary layers is estimated using the theoretical expression for the velocity field in the boundary layers, derived recently by Beckebanze et al. (J. Fluid Mech., vol. 841, 2018, pp. 614–635). In the linear regime, we show that the energy budget is closed, in the steady state and also in the transient regime, by taking into account the bulk dissipation and, more importantly, the dissipation in the boundary layers, without any adjustable parameters. The dependence of the different sources on the thickness of the experimental set-up is also discussed. In the nonlinear regime, the analysis is extended by estimating the dissipation due to the secondary waves generated by triadic resonant instabilities, showing the importance of the energy transfer from large scales to small scales. The method tested here on internal wave attractors can be generalized straightforwardly to any quasi-two-dimensional stratified flow.

JFM classification

Geophysical and Geological Flows: Internal waves Geophysical and Geological Flows: Stratified flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 880 , 10 December 2019 , pp. 743 - 763
Copyright
© 2019 Cambridge University Press 

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